Agree with smkettner. You really should have four batteries or you may drain past 50% DOD using the m/w. You probably should go with a 2.0 to 2.5 PSW inverter. Elaine has been asked several times "heard them m/w going and you're not hookedup!"
Aussies are far ahead of us in utilizing solar and lithium iron phosphate (LFP batteries since most of them are boondockers (word there seems to be "free campers"). One wrote me that they have 1200 W of panels and considerable LFP battery bank on their 24' camper. Brian Appleby has 1200 W on his pickup camper and trailer. combined. We have 1420 W and 9.5 kW-hr of LFP. We use solar/battery to run micro-wave, Dometic fridge etc. We have run a/c up to 3.5 hours. Aussies are adopting DC a/c (Fujitsu split level etc) which use only 750 W as opposed to 1500 to 1750 for a Dometic. We are looking into this. But, we are doing well with what we have so far. It is all a question of life style desires.
Solar panels are inexpensive. Don't think there is such a thing as "excessive" solar. Your controller will take care of avoiding over-charging or get a battery management system. "Excessive" means you will charge adequately under cloud cover or rain. But it shall not do you much good in full tree shadow.
Reed and Elaine